Properties

Label 177.9.c.a.58.19
Level $177$
Weight $9$
Character 177.58
Analytic conductor $72.106$
Analytic rank $0$
Dimension $80$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 177 = 3 \cdot 59 \)
Weight: \( k \) \(=\) \( 9 \)
Character orbit: \([\chi]\) \(=\) 177.c (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(72.1060139808\)
Analytic rank: \(0\)
Dimension: \(80\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 58.19
Character \(\chi\) \(=\) 177.58
Dual form 177.9.c.a.58.62

$q$-expansion

\(f(q)\) \(=\) \(q-19.3849i q^{2} +46.7654 q^{3} -119.774 q^{4} +778.298 q^{5} -906.541i q^{6} +1420.14 q^{7} -2640.73i q^{8} +2187.00 q^{9} +O(q^{10})\) \(q-19.3849i q^{2} +46.7654 q^{3} -119.774 q^{4} +778.298 q^{5} -906.541i q^{6} +1420.14 q^{7} -2640.73i q^{8} +2187.00 q^{9} -15087.2i q^{10} -18287.8i q^{11} -5601.26 q^{12} -10397.2i q^{13} -27529.1i q^{14} +36397.4 q^{15} -81852.3 q^{16} -79909.4 q^{17} -42394.7i q^{18} +126623. q^{19} -93219.5 q^{20} +66413.1 q^{21} -354507. q^{22} +166838. i q^{23} -123495. i q^{24} +215122. q^{25} -201548. q^{26} +102276. q^{27} -170095. q^{28} -83511.6 q^{29} -705559. i q^{30} -892019. i q^{31} +910670. i q^{32} -855236. i q^{33} +1.54903e6i q^{34} +1.10529e6 q^{35} -261945. q^{36} -612380. i q^{37} -2.45456e6i q^{38} -486228. i q^{39} -2.05528e6i q^{40} +889825. q^{41} -1.28741e6i q^{42} +1.51063e6i q^{43} +2.19040e6i q^{44} +1.70214e6 q^{45} +3.23414e6 q^{46} +514948. i q^{47} -3.82785e6 q^{48} -3.74802e6 q^{49} -4.17012e6i q^{50} -3.73699e6 q^{51} +1.24531e6i q^{52} +2.99146e6 q^{53} -1.98261e6i q^{54} -1.42333e7i q^{55} -3.75020e6i q^{56} +5.92155e6 q^{57} +1.61886e6i q^{58} +(1.09695e7 - 5.14778e6i) q^{59} -4.35945e6 q^{60} -1.64754e7i q^{61} -1.72917e7 q^{62} +3.10584e6 q^{63} -3.30096e6 q^{64} -8.09210e6i q^{65} -1.65786e7 q^{66} -6.55053e6i q^{67} +9.57104e6 q^{68} +7.80226e6i q^{69} -2.14259e7i q^{70} +4.70095e7 q^{71} -5.77528e6i q^{72} -1.51356e7i q^{73} -1.18709e7 q^{74} +1.00603e7 q^{75} -1.51660e7 q^{76} -2.59711e7i q^{77} -9.42547e6 q^{78} -1.57239e7 q^{79} -6.37055e7 q^{80} +4.78297e6 q^{81} -1.72491e7i q^{82} +4.55852e7i q^{83} -7.95454e6 q^{84} -6.21933e7 q^{85} +2.92833e7 q^{86} -3.90545e6 q^{87} -4.82932e7 q^{88} +1.04577e8i q^{89} -3.29957e7i q^{90} -1.47654e7i q^{91} -1.99828e7i q^{92} -4.17156e7i q^{93} +9.98221e6 q^{94} +9.85500e7 q^{95} +4.25878e7i q^{96} -7.35443e6i q^{97} +7.26549e7i q^{98} -3.99954e7i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 80q - 10240q^{4} + 160q^{7} + 174960q^{9} + O(q^{10}) \) \( 80q - 10240q^{4} + 160q^{7} + 174960q^{9} - 22680q^{12} - 59616q^{15} + 1199848q^{16} - 10608q^{17} - 27516q^{19} - 146436q^{20} - 974696q^{22} + 5718040q^{25} - 797484q^{26} - 3133000q^{28} + 1725924q^{29} + 4318800q^{35} - 22394880q^{36} - 732180q^{41} + 22752084q^{46} + 8703936q^{48} + 55899176q^{49} - 10373832q^{51} - 39265944q^{53} - 11408040q^{57} - 33575112q^{59} - 18034488q^{60} + 13038600q^{62} + 349920q^{63} - 241654260q^{64} - 35711928q^{66} + 36772608q^{68} - 235272660q^{71} - 63050712q^{74} + 74363184q^{75} + 9454680q^{76} - 10865988q^{78} + 17252580q^{79} + 318203976q^{80} + 382637520q^{81} - 20743128q^{84} - 27245820q^{85} + 105666984q^{86} + 29437992q^{87} + 82079788q^{88} + 121215992q^{94} - 690837276q^{95} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/177\mathbb{Z}\right)^\times\).

\(n\) \(61\) \(119\)
\(\chi(n)\) \(-1\) \(1\)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 19.3849i 1.21156i −0.795634 0.605778i \(-0.792862\pi\)
0.795634 0.605778i \(-0.207138\pi\)
\(3\) 46.7654 0.577350
\(4\) −119.774 −0.467866
\(5\) 778.298 1.24528 0.622638 0.782510i \(-0.286061\pi\)
0.622638 + 0.782510i \(0.286061\pi\)
\(6\) 906.541i 0.699492i
\(7\) 1420.14 0.591476 0.295738 0.955269i \(-0.404434\pi\)
0.295738 + 0.955269i \(0.404434\pi\)
\(8\) 2640.73i 0.644710i
\(9\) 2187.00 0.333333
\(10\) 15087.2i 1.50872i
\(11\) 18287.8i 1.24908i −0.780992 0.624541i \(-0.785286\pi\)
0.780992 0.624541i \(-0.214714\pi\)
\(12\) −5601.26 −0.270122
\(13\) 10397.2i 0.364034i −0.983295 0.182017i \(-0.941737\pi\)
0.983295 0.182017i \(-0.0582626\pi\)
\(14\) 27529.1i 0.716606i
\(15\) 36397.4 0.718961
\(16\) −81852.3 −1.24897
\(17\) −79909.4 −0.956758 −0.478379 0.878153i \(-0.658775\pi\)
−0.478379 + 0.878153i \(0.658775\pi\)
\(18\) 42394.7i 0.403852i
\(19\) 126623. 0.971620 0.485810 0.874064i \(-0.338525\pi\)
0.485810 + 0.874064i \(0.338525\pi\)
\(20\) −93219.5 −0.582622
\(21\) 66413.1 0.341489
\(22\) −354507. −1.51333
\(23\) 166838.i 0.596190i 0.954536 + 0.298095i \(0.0963512\pi\)
−0.954536 + 0.298095i \(0.903649\pi\)
\(24\) 123495.i 0.372224i
\(25\) 215122. 0.550713
\(26\) −201548. −0.441047
\(27\) 102276. 0.192450
\(28\) −170095. −0.276732
\(29\) −83511.6 −0.118074 −0.0590371 0.998256i \(-0.518803\pi\)
−0.0590371 + 0.998256i \(0.518803\pi\)
\(30\) 705559.i 0.871060i
\(31\) 892019.i 0.965889i −0.875651 0.482944i \(-0.839567\pi\)
0.875651 0.482944i \(-0.160433\pi\)
\(32\) 910670.i 0.868483i
\(33\) 855236.i 0.721157i
\(34\) 1.54903e6i 1.15917i
\(35\) 1.10529e6 0.736552
\(36\) −261945. −0.155955
\(37\) 612380.i 0.326749i −0.986564 0.163374i \(-0.947762\pi\)
0.986564 0.163374i \(-0.0522378\pi\)
\(38\) 2.45456e6i 1.17717i
\(39\) 486228.i 0.210175i
\(40\) 2.05528e6i 0.802842i
\(41\) 889825. 0.314897 0.157449 0.987527i \(-0.449673\pi\)
0.157449 + 0.987527i \(0.449673\pi\)
\(42\) 1.28741e6i 0.413733i
\(43\) 1.51063e6i 0.441859i 0.975290 + 0.220929i \(0.0709090\pi\)
−0.975290 + 0.220929i \(0.929091\pi\)
\(44\) 2.19040e6i 0.584402i
\(45\) 1.70214e6 0.415092
\(46\) 3.23414e6 0.722317
\(47\) 514948.i 0.105529i 0.998607 + 0.0527645i \(0.0168033\pi\)
−0.998607 + 0.0527645i \(0.983197\pi\)
\(48\) −3.82785e6 −0.721092
\(49\) −3.74802e6 −0.650156
\(50\) 4.17012e6i 0.667219i
\(51\) −3.73699e6 −0.552385
\(52\) 1.24531e6i 0.170319i
\(53\) 2.99146e6 0.379123 0.189562 0.981869i \(-0.439293\pi\)
0.189562 + 0.981869i \(0.439293\pi\)
\(54\) 1.98261e6i 0.233164i
\(55\) 1.42333e7i 1.55545i
\(56\) 3.75020e6i 0.381331i
\(57\) 5.92155e6 0.560965
\(58\) 1.61886e6i 0.143053i
\(59\) 1.09695e7 5.14778e6i 0.905275 0.424826i
\(60\) −4.35945e6 −0.336377
\(61\) 1.64754e7i 1.18992i −0.803756 0.594959i \(-0.797168\pi\)
0.803756 0.594959i \(-0.202832\pi\)
\(62\) −1.72917e7 −1.17023
\(63\) 3.10584e6 0.197159
\(64\) −3.30096e6 −0.196753
\(65\) 8.09210e6i 0.453323i
\(66\) −1.65786e7 −0.873722
\(67\) 6.55053e6i 0.325070i −0.986703 0.162535i \(-0.948033\pi\)
0.986703 0.162535i \(-0.0519671\pi\)
\(68\) 9.57104e6 0.447634
\(69\) 7.80226e6i 0.344211i
\(70\) 2.14259e7i 0.892373i
\(71\) 4.70095e7 1.84992 0.924959 0.380067i \(-0.124099\pi\)
0.924959 + 0.380067i \(0.124099\pi\)
\(72\) 5.77528e6i 0.214903i
\(73\) 1.51356e7i 0.532978i −0.963838 0.266489i \(-0.914136\pi\)
0.963838 0.266489i \(-0.0858637\pi\)
\(74\) −1.18709e7 −0.395874
\(75\) 1.00603e7 0.317954
\(76\) −1.51660e7 −0.454588
\(77\) 2.59711e7i 0.738802i
\(78\) −9.42547e6 −0.254639
\(79\) −1.57239e7 −0.403692 −0.201846 0.979417i \(-0.564694\pi\)
−0.201846 + 0.979417i \(0.564694\pi\)
\(80\) −6.37055e7 −1.55531
\(81\) 4.78297e6 0.111111
\(82\) 1.72491e7i 0.381515i
\(83\) 4.55852e7i 0.960532i 0.877123 + 0.480266i \(0.159460\pi\)
−0.877123 + 0.480266i \(0.840540\pi\)
\(84\) −7.95454e6 −0.159771
\(85\) −6.21933e7 −1.19143
\(86\) 2.92833e7 0.535336
\(87\) −3.90545e6 −0.0681701
\(88\) −4.82932e7 −0.805295
\(89\) 1.04577e8i 1.66678i 0.552688 + 0.833388i \(0.313602\pi\)
−0.552688 + 0.833388i \(0.686398\pi\)
\(90\) 3.29957e7i 0.502907i
\(91\) 1.47654e7i 0.215318i
\(92\) 1.99828e7i 0.278937i
\(93\) 4.17156e7i 0.557656i
\(94\) 9.98221e6 0.127854
\(95\) 9.85500e7 1.20994
\(96\) 4.25878e7i 0.501419i
\(97\) 7.35443e6i 0.0830735i −0.999137 0.0415367i \(-0.986775\pi\)
0.999137 0.0415367i \(-0.0132254\pi\)
\(98\) 7.26549e7i 0.787699i
\(99\) 3.99954e7i 0.416360i
\(100\) −2.57660e7 −0.257660
\(101\) 1.26697e7i 0.121753i −0.998145 0.0608767i \(-0.980610\pi\)
0.998145 0.0608767i \(-0.0193896\pi\)
\(102\) 7.24412e7i 0.669244i
\(103\) 1.08434e8i 0.963422i 0.876330 + 0.481711i \(0.159985\pi\)
−0.876330 + 0.481711i \(0.840015\pi\)
\(104\) −2.74562e7 −0.234696
\(105\) 5.16892e7 0.425248
\(106\) 5.79892e7i 0.459328i
\(107\) −7.77276e7 −0.592980 −0.296490 0.955036i \(-0.595816\pi\)
−0.296490 + 0.955036i \(0.595816\pi\)
\(108\) −1.22499e7 −0.0900408
\(109\) 2.41281e7i 0.170929i 0.996341 + 0.0854647i \(0.0272375\pi\)
−0.996341 + 0.0854647i \(0.972763\pi\)
\(110\) −2.75912e8 −1.88451
\(111\) 2.86382e7i 0.188648i
\(112\) −1.16241e8 −0.738735
\(113\) 1.55132e8i 0.951455i −0.879593 0.475728i \(-0.842185\pi\)
0.879593 0.475728i \(-0.157815\pi\)
\(114\) 1.14789e8i 0.679640i
\(115\) 1.29850e8i 0.742421i
\(116\) 1.00025e7 0.0552428
\(117\) 2.27386e7i 0.121345i
\(118\) −9.97890e7 2.12643e8i −0.514701 1.09679i
\(119\) −1.13482e8 −0.565900
\(120\) 9.61157e7i 0.463521i
\(121\) −1.20085e8 −0.560204
\(122\) −3.19374e8 −1.44165
\(123\) 4.16130e7 0.181806
\(124\) 1.06840e8i 0.451906i
\(125\) −1.36593e8 −0.559487
\(126\) 6.02062e7i 0.238869i
\(127\) −5.37223e7 −0.206509 −0.103255 0.994655i \(-0.532926\pi\)
−0.103255 + 0.994655i \(0.532926\pi\)
\(128\) 2.97120e8i 1.10686i
\(129\) 7.06450e7i 0.255107i
\(130\) −1.56864e8 −0.549226
\(131\) 3.29311e8i 1.11820i 0.829099 + 0.559101i \(0.188854\pi\)
−0.829099 + 0.559101i \(0.811146\pi\)
\(132\) 1.02435e8i 0.337405i
\(133\) 1.79821e8 0.574691
\(134\) −1.26981e8 −0.393840
\(135\) 7.96011e7 0.239654
\(136\) 2.11019e8i 0.616832i
\(137\) −5.67910e8 −1.61212 −0.806059 0.591835i \(-0.798404\pi\)
−0.806059 + 0.591835i \(0.798404\pi\)
\(138\) 1.51246e8 0.417030
\(139\) −1.08782e7 −0.0291405 −0.0145702 0.999894i \(-0.504638\pi\)
−0.0145702 + 0.999894i \(0.504638\pi\)
\(140\) −1.32384e8 −0.344607
\(141\) 2.40817e7i 0.0609272i
\(142\) 9.11274e8i 2.24128i
\(143\) −1.90141e8 −0.454708
\(144\) −1.79011e8 −0.416322
\(145\) −6.49969e7 −0.147035
\(146\) −2.93403e8 −0.645733
\(147\) −1.75277e8 −0.375367
\(148\) 7.33469e7i 0.152875i
\(149\) 1.46320e8i 0.296865i 0.988923 + 0.148432i \(0.0474228\pi\)
−0.988923 + 0.148432i \(0.952577\pi\)
\(150\) 1.95017e8i 0.385219i
\(151\) 1.73523e8i 0.333771i −0.985976 0.166885i \(-0.946629\pi\)
0.985976 0.166885i \(-0.0533710\pi\)
\(152\) 3.34376e8i 0.626413i
\(153\) −1.74762e8 −0.318919
\(154\) −5.03448e8 −0.895100
\(155\) 6.94256e8i 1.20280i
\(156\) 5.82372e7i 0.0983337i
\(157\) 7.72308e8i 1.27114i −0.772045 0.635568i \(-0.780766\pi\)
0.772045 0.635568i \(-0.219234\pi\)
\(158\) 3.04805e8i 0.489096i
\(159\) 1.39897e8 0.218887
\(160\) 7.08772e8i 1.08150i
\(161\) 2.36933e8i 0.352632i
\(162\) 9.27173e7i 0.134617i
\(163\) 1.04794e9 1.48452 0.742261 0.670111i \(-0.233754\pi\)
0.742261 + 0.670111i \(0.233754\pi\)
\(164\) −1.06578e8 −0.147330
\(165\) 6.65628e8i 0.898040i
\(166\) 8.83664e8 1.16374
\(167\) −3.62072e8 −0.465510 −0.232755 0.972535i \(-0.574774\pi\)
−0.232755 + 0.972535i \(0.574774\pi\)
\(168\) 1.75379e8i 0.220161i
\(169\) 7.07629e8 0.867479
\(170\) 1.20561e9i 1.44348i
\(171\) 2.76923e8 0.323873
\(172\) 1.80933e8i 0.206731i
\(173\) 5.60602e8i 0.625850i −0.949778 0.312925i \(-0.898691\pi\)
0.949778 0.312925i \(-0.101309\pi\)
\(174\) 7.57067e7i 0.0825919i
\(175\) 3.05503e8 0.325734
\(176\) 1.49690e9i 1.56006i
\(177\) 5.12995e8 2.40738e8i 0.522661 0.245274i
\(178\) 2.02722e9 2.01939
\(179\) 1.26287e8i 0.123011i −0.998107 0.0615056i \(-0.980410\pi\)
0.998107 0.0615056i \(-0.0195902\pi\)
\(180\) −2.03871e8 −0.194207
\(181\) 1.21141e9 1.12869 0.564346 0.825539i \(-0.309129\pi\)
0.564346 + 0.825539i \(0.309129\pi\)
\(182\) −2.86225e8 −0.260869
\(183\) 7.70479e8i 0.687000i
\(184\) 4.40576e8 0.384370
\(185\) 4.76614e8i 0.406892i
\(186\) −8.08651e8 −0.675631
\(187\) 1.46137e9i 1.19507i
\(188\) 6.16772e7i 0.0493734i
\(189\) 1.45246e8 0.113830
\(190\) 1.91038e9i 1.46590i
\(191\) 7.94897e8i 0.597279i 0.954366 + 0.298640i \(0.0965329\pi\)
−0.954366 + 0.298640i \(0.903467\pi\)
\(192\) −1.54371e8 −0.113595
\(193\) −4.07982e8 −0.294043 −0.147022 0.989133i \(-0.546969\pi\)
−0.147022 + 0.989133i \(0.546969\pi\)
\(194\) −1.42565e8 −0.100648
\(195\) 3.78430e8i 0.261726i
\(196\) 4.48914e8 0.304185
\(197\) 1.98553e9 1.31829 0.659145 0.752015i \(-0.270918\pi\)
0.659145 + 0.752015i \(0.270918\pi\)
\(198\) −7.75306e8 −0.504444
\(199\) 8.20394e7 0.0523130 0.0261565 0.999658i \(-0.491673\pi\)
0.0261565 + 0.999658i \(0.491673\pi\)
\(200\) 5.68080e8i 0.355050i
\(201\) 3.06338e8i 0.187679i
\(202\) −2.45601e8 −0.147511
\(203\) −1.18598e8 −0.0698381
\(204\) 4.47593e8 0.258442
\(205\) 6.92548e8 0.392134
\(206\) 2.10198e9 1.16724
\(207\) 3.64876e8i 0.198730i
\(208\) 8.51033e8i 0.454667i
\(209\) 2.31565e9i 1.21363i
\(210\) 1.00199e9i 0.515212i
\(211\) 3.26356e9i 1.64650i −0.567679 0.823250i \(-0.692159\pi\)
0.567679 0.823250i \(-0.307841\pi\)
\(212\) −3.58298e8 −0.177379
\(213\) 2.19842e9 1.06805
\(214\) 1.50674e9i 0.718428i
\(215\) 1.17572e9i 0.550236i
\(216\) 2.70083e8i 0.124075i
\(217\) 1.26679e9i 0.571300i
\(218\) 4.67720e8 0.207090
\(219\) 7.07824e8i 0.307715i
\(220\) 1.70478e9i 0.727742i
\(221\) 8.30832e8i 0.348292i
\(222\) −5.55147e8 −0.228558
\(223\) −4.17801e9 −1.68947 −0.844735 0.535186i \(-0.820242\pi\)
−0.844735 + 0.535186i \(0.820242\pi\)
\(224\) 1.29327e9i 0.513687i
\(225\) 4.70472e8 0.183571
\(226\) −3.00722e9 −1.15274
\(227\) 4.74441e8i 0.178681i 0.996001 + 0.0893406i \(0.0284760\pi\)
−0.996001 + 0.0893406i \(0.971524\pi\)
\(228\) −7.09245e8 −0.262456
\(229\) 3.53819e8i 0.128659i 0.997929 + 0.0643293i \(0.0204908\pi\)
−0.997929 + 0.0643293i \(0.979509\pi\)
\(230\) 2.51713e9 0.899484
\(231\) 1.21455e9i 0.426548i
\(232\) 2.20532e8i 0.0761236i
\(233\) 4.54456e9i 1.54194i 0.636871 + 0.770971i \(0.280229\pi\)
−0.636871 + 0.770971i \(0.719771\pi\)
\(234\) −4.40785e8 −0.147016
\(235\) 4.00783e8i 0.131413i
\(236\) −1.31386e9 + 6.16568e8i −0.423547 + 0.198762i
\(237\) −7.35332e8 −0.233072
\(238\) 2.19984e9i 0.685619i
\(239\) −3.88537e8 −0.119080 −0.0595402 0.998226i \(-0.518963\pi\)
−0.0595402 + 0.998226i \(0.518963\pi\)
\(240\) −2.97921e9 −0.897958
\(241\) 4.20396e9 1.24621 0.623104 0.782139i \(-0.285871\pi\)
0.623104 + 0.782139i \(0.285871\pi\)
\(242\) 2.32783e9i 0.678718i
\(243\) 2.23677e8 0.0641500
\(244\) 1.97332e9i 0.556722i
\(245\) −2.91707e9 −0.809623
\(246\) 8.06663e8i 0.220268i
\(247\) 1.31652e9i 0.353703i
\(248\) −2.35558e9 −0.622718
\(249\) 2.13181e9i 0.554563i
\(250\) 2.64785e9i 0.677849i
\(251\) −3.15846e9 −0.795758 −0.397879 0.917438i \(-0.630254\pi\)
−0.397879 + 0.917438i \(0.630254\pi\)
\(252\) −3.71997e8 −0.0922438
\(253\) 3.05111e9 0.744690
\(254\) 1.04140e9i 0.250197i
\(255\) −2.90849e9 −0.687871
\(256\) 4.91460e9 1.14427
\(257\) 2.22549e8 0.0510144 0.0255072 0.999675i \(-0.491880\pi\)
0.0255072 + 0.999675i \(0.491880\pi\)
\(258\) 1.36945e9 0.309076
\(259\) 8.69662e8i 0.193264i
\(260\) 9.69220e8i 0.212094i
\(261\) −1.82640e8 −0.0393581
\(262\) 6.38365e9 1.35476
\(263\) 6.28171e9 1.31297 0.656485 0.754339i \(-0.272043\pi\)
0.656485 + 0.754339i \(0.272043\pi\)
\(264\) −2.25845e9 −0.464937
\(265\) 2.32825e9 0.472113
\(266\) 3.48581e9i 0.696269i
\(267\) 4.89059e9i 0.962314i
\(268\) 7.84580e8i 0.152089i
\(269\) 5.04341e9i 0.963198i 0.876392 + 0.481599i \(0.159944\pi\)
−0.876392 + 0.481599i \(0.840056\pi\)
\(270\) 1.54306e9i 0.290353i
\(271\) 8.39347e9 1.55620 0.778098 0.628143i \(-0.216185\pi\)
0.778098 + 0.628143i \(0.216185\pi\)
\(272\) 6.54077e9 1.19496
\(273\) 6.90509e8i 0.124314i
\(274\) 1.10089e10i 1.95317i
\(275\) 3.93411e9i 0.687885i
\(276\) 9.34505e8i 0.161044i
\(277\) 3.66227e9 0.622058 0.311029 0.950400i \(-0.399326\pi\)
0.311029 + 0.950400i \(0.399326\pi\)
\(278\) 2.10872e8i 0.0353053i
\(279\) 1.95084e9i 0.321963i
\(280\) 2.91877e9i 0.474862i
\(281\) −1.53163e8 −0.0245656 −0.0122828 0.999925i \(-0.503910\pi\)
−0.0122828 + 0.999925i \(0.503910\pi\)
\(282\) 4.66822e8 0.0738167
\(283\) 1.25501e9i 0.195660i 0.995203 + 0.0978298i \(0.0311901\pi\)
−0.995203 + 0.0978298i \(0.968810\pi\)
\(284\) −5.63050e9 −0.865513
\(285\) 4.60873e9 0.698557
\(286\) 3.68587e9i 0.550904i
\(287\) 1.26367e9 0.186254
\(288\) 1.99164e9i 0.289494i
\(289\) −5.90246e8 −0.0846139
\(290\) 1.25996e9i 0.178141i
\(291\) 3.43933e8i 0.0479625i
\(292\) 1.81285e9i 0.249362i
\(293\) −4.99360e8 −0.0677553 −0.0338777 0.999426i \(-0.510786\pi\)
−0.0338777 + 0.999426i \(0.510786\pi\)
\(294\) 3.39773e9i 0.454778i
\(295\) 8.53757e9 4.00650e9i 1.12732 0.529026i
\(296\) −1.61713e9 −0.210658
\(297\) 1.87040e9i 0.240386i
\(298\) 2.83640e9 0.359668
\(299\) 1.73465e9 0.217033
\(300\) −1.20495e9 −0.148760
\(301\) 2.14529e9i 0.261349i
\(302\) −3.36371e9 −0.404382
\(303\) 5.92504e8i 0.0702944i
\(304\) −1.03643e10 −1.21352
\(305\) 1.28228e10i 1.48178i
\(306\) 3.38774e9i 0.386388i
\(307\) −2.09107e9 −0.235404 −0.117702 0.993049i \(-0.537553\pi\)
−0.117702 + 0.993049i \(0.537553\pi\)
\(308\) 3.11066e9i 0.345660i
\(309\) 5.07096e9i 0.556232i
\(310\) −1.34581e10 −1.45726
\(311\) −4.28031e9 −0.457545 −0.228773 0.973480i \(-0.573471\pi\)
−0.228773 + 0.973480i \(0.573471\pi\)
\(312\) −1.28400e9 −0.135502
\(313\) 9.82280e8i 0.102343i 0.998690 + 0.0511715i \(0.0162955\pi\)
−0.998690 + 0.0511715i \(0.983704\pi\)
\(314\) −1.49711e10 −1.54005
\(315\) 2.41726e9 0.245517
\(316\) 1.88330e9 0.188874
\(317\) 6.67356e9 0.660877 0.330438 0.943828i \(-0.392803\pi\)
0.330438 + 0.943828i \(0.392803\pi\)
\(318\) 2.71188e9i 0.265193i
\(319\) 1.52724e9i 0.147484i
\(320\) −2.56913e9 −0.245012
\(321\) −3.63496e9 −0.342357
\(322\) 4.59292e9 0.427234
\(323\) −1.01183e10 −0.929606
\(324\) −5.72873e8 −0.0519851
\(325\) 2.23666e9i 0.200478i
\(326\) 2.03142e10i 1.79858i
\(327\) 1.12836e9i 0.0986862i
\(328\) 2.34979e9i 0.203017i
\(329\) 7.31296e8i 0.0624180i
\(330\) −1.29031e10 −1.08803
\(331\) 1.51469e10 1.26186 0.630932 0.775838i \(-0.282673\pi\)
0.630932 + 0.775838i \(0.282673\pi\)
\(332\) 5.45991e9i 0.449400i
\(333\) 1.33927e9i 0.108916i
\(334\) 7.01873e9i 0.563991i
\(335\) 5.09826e9i 0.404802i
\(336\) −5.43607e9 −0.426509
\(337\) 1.33007e10i 1.03123i 0.856821 + 0.515613i \(0.172436\pi\)
−0.856821 + 0.515613i \(0.827564\pi\)
\(338\) 1.37173e10i 1.05100i
\(339\) 7.25482e9i 0.549323i
\(340\) 7.44911e9 0.557428
\(341\) −1.63131e10 −1.20647
\(342\) 5.36813e9i 0.392390i
\(343\) −1.35095e10 −0.976028
\(344\) 3.98916e9 0.284871
\(345\) 6.07248e9i 0.428637i
\(346\) −1.08672e10 −0.758252
\(347\) 5.23308e9i 0.360943i −0.983580 0.180472i \(-0.942238\pi\)
0.983580 0.180472i \(-0.0577624\pi\)
\(348\) 4.67770e8 0.0318945
\(349\) 4.17787e9i 0.281613i 0.990037 + 0.140807i \(0.0449696\pi\)
−0.990037 + 0.140807i \(0.955030\pi\)
\(350\) 5.92213e9i 0.394644i
\(351\) 1.06338e9i 0.0700584i
\(352\) 1.66542e10 1.08481
\(353\) 3.00966e10i 1.93829i −0.246496 0.969144i \(-0.579279\pi\)
0.246496 0.969144i \(-0.420721\pi\)
\(354\) −4.66667e9 9.94434e9i −0.297163 0.633232i
\(355\) 3.65874e10 2.30366
\(356\) 1.25256e10i 0.779827i
\(357\) −5.30703e9 −0.326722
\(358\) −2.44805e9 −0.149035
\(359\) −2.38260e10 −1.43441 −0.717204 0.696863i \(-0.754578\pi\)
−0.717204 + 0.696863i \(0.754578\pi\)
\(360\) 4.49489e9i 0.267614i
\(361\) −9.50298e8 −0.0559540
\(362\) 2.34829e10i 1.36747i
\(363\) −5.61580e9 −0.323434
\(364\) 1.76850e9i 0.100740i
\(365\) 1.17800e10i 0.663705i
\(366\) −1.49356e10 −0.832338
\(367\) 1.87371e10i 1.03285i 0.856333 + 0.516425i \(0.172737\pi\)
−0.856333 + 0.516425i \(0.827263\pi\)
\(368\) 1.36561e10i 0.744622i
\(369\) 1.94605e9 0.104966
\(370\) −9.23910e9 −0.492973
\(371\) 4.24828e9 0.224242
\(372\) 4.99642e9i 0.260908i
\(373\) −1.85649e10 −0.959083 −0.479541 0.877519i \(-0.659197\pi\)
−0.479541 + 0.877519i \(0.659197\pi\)
\(374\) 2.83284e10 1.44789
\(375\) −6.38784e9 −0.323020
\(376\) 1.35984e9 0.0680357
\(377\) 8.68285e8i 0.0429830i
\(378\) 2.81557e9i 0.137911i
\(379\) 6.06903e9 0.294146 0.147073 0.989126i \(-0.453015\pi\)
0.147073 + 0.989126i \(0.453015\pi\)
\(380\) −1.18037e10 −0.566087
\(381\) −2.51234e9 −0.119228
\(382\) 1.54090e10 0.723637
\(383\) 2.33300e10 1.08423 0.542113 0.840305i \(-0.317624\pi\)
0.542113 + 0.840305i \(0.317624\pi\)
\(384\) 1.38949e10i 0.639046i
\(385\) 2.02133e10i 0.920013i
\(386\) 7.90868e9i 0.356250i
\(387\) 3.30374e9i 0.147286i
\(388\) 8.80867e8i 0.0388672i
\(389\) 1.13812e10 0.497037 0.248518 0.968627i \(-0.420056\pi\)
0.248518 + 0.968627i \(0.420056\pi\)
\(390\) −7.33582e9 −0.317096
\(391\) 1.33320e10i 0.570410i
\(392\) 9.89751e9i 0.419162i
\(393\) 1.54003e10i 0.645595i
\(394\) 3.84892e10i 1.59718i
\(395\) −1.22378e10 −0.502709
\(396\) 4.79039e9i 0.194801i
\(397\) 2.41950e10i 0.974009i 0.873399 + 0.487005i \(0.161911\pi\)
−0.873399 + 0.487005i \(0.838089\pi\)
\(398\) 1.59032e9i 0.0633801i
\(399\) 8.40940e9 0.331798
\(400\) −1.76083e10 −0.687822
\(401\) 3.34160e10i 1.29234i 0.763194 + 0.646170i \(0.223630\pi\)
−0.763194 + 0.646170i \(0.776370\pi\)
\(402\) −5.93832e9 −0.227384
\(403\) −9.27447e9 −0.351616
\(404\) 1.51750e9i 0.0569642i
\(405\) 3.72257e9 0.138364
\(406\) 2.29900e9i 0.0846127i
\(407\) −1.11991e10 −0.408136
\(408\) 9.86840e9i 0.356128i
\(409\) 1.77855e8i 0.00635583i 0.999995 + 0.00317791i \(0.00101156\pi\)
−0.999995 + 0.00317791i \(0.998988\pi\)
\(410\) 1.34250e10i 0.475092i
\(411\) −2.65585e10 −0.930757
\(412\) 1.29875e10i 0.450752i
\(413\) 1.55782e10 7.31054e9i 0.535449 0.251275i
\(414\) 7.07307e9 0.240772
\(415\) 3.54789e10i 1.19613i
\(416\) 9.46840e9 0.316157
\(417\) −5.08721e8 −0.0168243
\(418\) −4.48885e10 −1.47038
\(419\) 5.25728e10i 1.70571i 0.522148 + 0.852855i \(0.325131\pi\)
−0.522148 + 0.852855i \(0.674869\pi\)
\(420\) −6.19100e9 −0.198959
\(421\) 3.56037e10i 1.13336i 0.823939 + 0.566679i \(0.191772\pi\)
−0.823939 + 0.566679i \(0.808228\pi\)
\(422\) −6.32637e10 −1.99483
\(423\) 1.12619e9i 0.0351764i
\(424\) 7.89965e9i 0.244424i
\(425\) −1.71903e10 −0.526899
\(426\) 4.26161e10i 1.29400i
\(427\) 2.33973e10i 0.703809i
\(428\) 9.30971e9 0.277435
\(429\) −8.89204e9 −0.262526
\(430\) 2.27911e10 0.666641
\(431\) 6.55302e10i 1.89903i −0.313716 0.949517i \(-0.601574\pi\)
0.313716 0.949517i \(-0.398426\pi\)
\(432\) −8.37152e9 −0.240364
\(433\) 4.06255e10 1.15571 0.577853 0.816141i \(-0.303891\pi\)
0.577853 + 0.816141i \(0.303891\pi\)
\(434\) −2.45565e10 −0.692162
\(435\) −3.03960e9 −0.0848907
\(436\) 2.88991e9i 0.0799720i
\(437\) 2.11255e10i 0.579270i
\(438\) −1.37211e10 −0.372814
\(439\) 1.20990e10 0.325757 0.162878 0.986646i \(-0.447922\pi\)
0.162878 + 0.986646i \(0.447922\pi\)
\(440\) −3.75865e10 −1.00282
\(441\) −8.19691e9 −0.216719
\(442\) 1.61056e10 0.421976
\(443\) 2.49302e10i 0.647307i 0.946176 + 0.323654i \(0.104911\pi\)
−0.946176 + 0.323654i \(0.895089\pi\)
\(444\) 3.43010e9i 0.0882621i
\(445\) 8.13922e10i 2.07560i
\(446\) 8.09903e10i 2.04688i
\(447\) 6.84271e9i 0.171395i
\(448\) −4.68782e9 −0.116375
\(449\) 4.83662e10 1.19003 0.595013 0.803716i \(-0.297147\pi\)
0.595013 + 0.803716i \(0.297147\pi\)
\(450\) 9.12005e9i 0.222406i
\(451\) 1.62729e10i 0.393332i
\(452\) 1.85807e10i 0.445153i
\(453\) 8.11485e9i 0.192703i
\(454\) 9.19698e9 0.216482
\(455\) 1.14919e10i 0.268130i
\(456\) 1.56372e10i 0.361660i
\(457\) 1.22137e10i 0.280017i 0.990150 + 0.140008i \(0.0447129\pi\)
−0.990150 + 0.140008i \(0.955287\pi\)
\(458\) 6.85873e9 0.155877
\(459\) −8.17280e9 −0.184128
\(460\) 1.55526e10i 0.347353i
\(461\) 1.05023e10 0.232530 0.116265 0.993218i \(-0.462908\pi\)
0.116265 + 0.993218i \(0.462908\pi\)
\(462\) −2.35439e10 −0.516786
\(463\) 1.84192e10i 0.400817i 0.979712 + 0.200408i \(0.0642269\pi\)
−0.979712 + 0.200408i \(0.935773\pi\)
\(464\) 6.83562e9 0.147471
\(465\) 3.24671e10i 0.694436i
\(466\) 8.80957e10 1.86815
\(467\) 5.99569e10i 1.26058i 0.776358 + 0.630292i \(0.217065\pi\)
−0.776358 + 0.630292i \(0.782935\pi\)
\(468\) 2.72349e9i 0.0567730i
\(469\) 9.30263e9i 0.192271i
\(470\) 7.76913e9 0.159214
\(471\) 3.61173e10i 0.733891i
\(472\) −1.35939e10 2.89676e10i −0.273890 0.583640i
\(473\) 2.76260e10 0.551917
\(474\) 1.42543e10i 0.282379i
\(475\) 2.72393e10 0.535084
\(476\) 1.35922e10 0.264765
\(477\) 6.54233e9 0.126374
\(478\) 7.53173e9i 0.144272i
\(479\) −7.23437e10 −1.37423 −0.687114 0.726550i \(-0.741123\pi\)
−0.687114 + 0.726550i \(0.741123\pi\)
\(480\) 3.31460e10i 0.624405i
\(481\) −6.36702e9 −0.118948
\(482\) 8.14933e10i 1.50985i
\(483\) 1.10803e10i 0.203592i
\(484\) 1.43830e10 0.262100
\(485\) 5.72394e9i 0.103449i
\(486\) 4.33596e9i 0.0777213i
\(487\) 1.33799e10 0.237869 0.118934 0.992902i \(-0.462052\pi\)
0.118934 + 0.992902i \(0.462052\pi\)
\(488\) −4.35072e10 −0.767152
\(489\) 4.90074e10 0.857089
\(490\) 5.65471e10i 0.980903i
\(491\) 7.07239e10 1.21686 0.608429 0.793608i \(-0.291800\pi\)
0.608429 + 0.793608i \(0.291800\pi\)
\(492\) −4.98414e9 −0.0850608
\(493\) 6.67336e9 0.112968
\(494\) −2.55205e10 −0.428530
\(495\) 3.11283e10i 0.518484i
\(496\) 7.30138e10i 1.20636i
\(497\) 6.67599e10 1.09418
\(498\) 4.13249e10 0.671884
\(499\) −6.14004e10 −0.990305 −0.495152 0.868806i \(-0.664888\pi\)
−0.495152 + 0.868806i \(0.664888\pi\)
\(500\) 1.63603e10 0.261765
\(501\) −1.69324e10 −0.268762
\(502\) 6.12265e10i 0.964105i
\(503\) 4.03520e10i 0.630367i 0.949031 + 0.315184i \(0.102066\pi\)
−0.949031 + 0.315184i \(0.897934\pi\)
\(504\) 8.20168e9i 0.127110i
\(505\) 9.86080e9i 0.151617i
\(506\) 5.91454e10i 0.902233i
\(507\) 3.30926e10 0.500839
\(508\) 6.43451e9 0.0966186
\(509\) 2.92932e10i 0.436412i 0.975903 + 0.218206i \(0.0700204\pi\)
−0.975903 + 0.218206i \(0.929980\pi\)
\(510\) 5.63808e10i 0.833394i
\(511\) 2.14947e10i 0.315244i
\(512\) 1.92060e10i 0.279485i
\(513\) 1.29504e10 0.186988
\(514\) 4.31408e9i 0.0618067i
\(515\) 8.43939e10i 1.19973i
\(516\) 8.46141e9i 0.119356i
\(517\) 9.41727e9 0.131814
\(518\) −1.68583e10 −0.234150
\(519\) 2.62168e10i 0.361335i
\(520\) −2.13691e10 −0.292262
\(521\) −2.11690e10 −0.287309 −0.143655 0.989628i \(-0.545885\pi\)
−0.143655 + 0.989628i \(0.545885\pi\)
\(522\) 3.54045e9i 0.0476844i
\(523\) 4.96188e10 0.663193 0.331596 0.943421i \(-0.392413\pi\)
0.331596 + 0.943421i \(0.392413\pi\)
\(524\) 3.94427e10i 0.523169i
\(525\) 1.42869e10 0.188062
\(526\) 1.21770e11i 1.59074i
\(527\) 7.12807e10i 0.924122i
\(528\) 7.00030e10i 0.900702i
\(529\) 5.04759e10 0.644557
\(530\) 4.51328e10i 0.571991i
\(531\) 2.39904e10 1.12582e10i 0.301758 0.141609i
\(532\) −2.15378e10 −0.268878
\(533\) 9.25166e9i 0.114633i
\(534\) 9.48036e10 1.16590
\(535\) −6.04952e10 −0.738424
\(536\) −1.72982e10 −0.209576
\(537\) 5.90584e9i 0.0710206i
\(538\) 9.77660e10 1.16697
\(539\) 6.85430e10i 0.812097i
\(540\) −9.53411e9 −0.112126
\(541\) 9.36324e10i 1.09304i 0.837445 + 0.546521i \(0.184048\pi\)
−0.837445 + 0.546521i \(0.815952\pi\)
\(542\) 1.62706e11i 1.88542i
\(543\) 5.66518e10 0.651650
\(544\) 7.27711e10i 0.830928i
\(545\) 1.87788e10i 0.212854i
\(546\) −1.33854e10 −0.150613
\(547\) 1.06216e11 1.18643 0.593214 0.805045i \(-0.297859\pi\)
0.593214 + 0.805045i \(0.297859\pi\)
\(548\) 6.80206e10 0.754255
\(549\) 3.60317e10i 0.396639i
\(550\) −7.62623e10 −0.833411
\(551\) −1.05745e10 −0.114723
\(552\) 2.06037e10 0.221916
\(553\) −2.23300e10 −0.238775
\(554\) 7.09926e10i 0.753658i
\(555\) 2.22890e10i 0.234919i
\(556\) 1.30292e9 0.0136338
\(557\) 8.42642e10 0.875432 0.437716 0.899113i \(-0.355787\pi\)
0.437716 + 0.899113i \(0.355787\pi\)
\(558\) −3.78169e10 −0.390076
\(559\) 1.57063e10 0.160852
\(560\) −9.04704e10 −0.919929
\(561\) 6.83414e10i 0.689973i
\(562\) 2.96904e9i 0.0297626i
\(563\) 6.64019e10i 0.660917i 0.943820 + 0.330459i \(0.107203\pi\)
−0.943820 + 0.330459i \(0.892797\pi\)
\(564\) 2.88436e9i 0.0285058i
\(565\) 1.20739e11i 1.18482i
\(566\) 2.43282e10 0.237052
\(567\) 6.79246e9 0.0657196
\(568\) 1.24140e11i 1.19266i
\(569\) 1.72792e11i 1.64845i 0.566262 + 0.824225i \(0.308389\pi\)
−0.566262 + 0.824225i \(0.691611\pi\)
\(570\) 8.93396e10i 0.846340i
\(571\) 1.22882e11i 1.15597i −0.816049 0.577983i \(-0.803840\pi\)
0.816049 0.577983i \(-0.196160\pi\)
\(572\) 2.27739e10 0.212742
\(573\) 3.71737e10i 0.344839i
\(574\) 2.44961e10i 0.225657i
\(575\) 3.58907e10i 0.328330i
\(576\) −7.21921e9 −0.0655843
\(577\) 1.51928e11 1.37068 0.685338 0.728225i \(-0.259655\pi\)
0.685338 + 0.728225i \(0.259655\pi\)
\(578\) 1.14418e10i 0.102514i
\(579\) −1.90794e10 −0.169766
\(580\) 7.78491e9 0.0687926
\(581\) 6.47372e10i 0.568132i
\(582\) −6.66710e9 −0.0581092
\(583\) 5.47073e10i 0.473555i
\(584\) −3.99692e10 −0.343617
\(585\) 1.76974e10i 0.151108i
\(586\) 9.68004e9i 0.0820893i
\(587\) 1.86857e11i 1.57382i 0.617065 + 0.786912i \(0.288322\pi\)
−0.617065 + 0.786912i \(0.711678\pi\)
\(588\) 2.09936e10 0.175622
\(589\) 1.12950e11i 0.938477i
\(590\) −7.76655e10 1.65500e11i −0.640944 1.36581i
\(591\) 9.28540e10 0.761116
\(592\) 5.01247e10i 0.408099i
\(593\) 9.07280e9 0.0733707 0.0366853 0.999327i \(-0.488320\pi\)
0.0366853 + 0.999327i \(0.488320\pi\)
\(594\) −3.62575e10 −0.291241
\(595\) −8.83229e10 −0.704702
\(596\) 1.75253e10i 0.138893i
\(597\) 3.83660e9 0.0302029
\(598\) 3.36260e10i 0.262948i
\(599\) 1.34106e10 0.104169 0.0520847 0.998643i \(-0.483413\pi\)
0.0520847 + 0.998643i \(0.483413\pi\)
\(600\) 2.65665e10i 0.204988i
\(601\) 2.00866e11i 1.53960i −0.638286 0.769799i \(-0.720356\pi\)
0.638286 0.769799i \(-0.279644\pi\)
\(602\) 4.15863e10 0.316639
\(603\) 1.43260e10i 0.108357i
\(604\) 2.07834e10i 0.156160i
\(605\) −9.34616e10 −0.697609
\(606\) −1.14856e10 −0.0851655
\(607\) 8.10048e10 0.596700 0.298350 0.954457i \(-0.403564\pi\)
0.298350 + 0.954457i \(0.403564\pi\)
\(608\) 1.15311e11i 0.843835i
\(609\) −5.54627e9 −0.0403210
\(610\) −2.48568e11 −1.79525
\(611\) 5.35401e9 0.0384162
\(612\) 2.09319e10 0.149211
\(613\) 7.91202e10i 0.560332i −0.959952 0.280166i \(-0.909611\pi\)
0.959952 0.280166i \(-0.0903895\pi\)
\(614\) 4.05351e10i 0.285205i
\(615\) 3.23873e10 0.226399
\(616\) −6.85828e10 −0.476313
\(617\) −1.16447e10 −0.0803504 −0.0401752 0.999193i \(-0.512792\pi\)
−0.0401752 + 0.999193i \(0.512792\pi\)
\(618\) 9.82999e10 0.673906
\(619\) 6.18871e10 0.421539 0.210769 0.977536i \(-0.432403\pi\)
0.210769 + 0.977536i \(0.432403\pi\)
\(620\) 8.31535e10i 0.562748i
\(621\) 1.70635e10i 0.114737i
\(622\) 8.29734e10i 0.554341i
\(623\) 1.48514e11i 0.985859i
\(624\) 3.97989e10i 0.262502i
\(625\) −1.90342e11 −1.24743
\(626\) 1.90414e10 0.123994
\(627\) 1.08292e11i 0.700691i
\(628\) 9.25021e10i 0.594721i
\(629\) 4.89349e10i 0.312620i
\(630\) 4.68584e10i 0.297458i
\(631\) −1.05029e11 −0.662506 −0.331253 0.943542i \(-0.607471\pi\)
−0.331253 + 0.943542i \(0.607471\pi\)
\(632\) 4.15225e10i 0.260265i
\(633\) 1.52622e11i 0.950607i
\(634\) 1.29366e11i 0.800688i
\(635\) −4.18119e10 −0.257161
\(636\) −1.67560e10 −0.102410
\(637\) 3.89688e10i 0.236679i
\(638\) 2.96054e10 0.178685
\(639\) 1.02810e11 0.616639
\(640\) 2.31248e11i 1.37835i
\(641\) 1.28978e11 0.763982 0.381991 0.924166i \(-0.375239\pi\)
0.381991 + 0.924166i \(0.375239\pi\)
\(642\) 7.04633e10i 0.414785i
\(643\) 1.03531e11 0.605657 0.302829 0.953045i \(-0.402069\pi\)
0.302829 + 0.953045i \(0.402069\pi\)
\(644\) 2.83783e10i 0.164985i
\(645\) 5.49829e10i 0.317679i
\(646\) 1.96143e11i 1.12627i
\(647\) 7.53363e10 0.429920 0.214960 0.976623i \(-0.431038\pi\)
0.214960 + 0.976623i \(0.431038\pi\)
\(648\) 1.26305e10i 0.0716345i
\(649\) −9.41415e10 2.00609e11i −0.530643 1.13076i
\(650\) −4.33574e10 −0.242890
\(651\) 5.92418e10i 0.329840i
\(652\) −1.25516e11 −0.694556
\(653\) 1.58411e11 0.871228 0.435614 0.900134i \(-0.356531\pi\)
0.435614 + 0.900134i \(0.356531\pi\)
\(654\) 2.18731e10 0.119564
\(655\) 2.56302e11i 1.39247i
\(656\) −7.28342e10 −0.393297
\(657\) 3.31017e10i 0.177659i
\(658\) 1.41761e10 0.0756228
\(659\) 9.20311e10i 0.487970i 0.969779 + 0.243985i \(0.0784548\pi\)
−0.969779 + 0.243985i \(0.921545\pi\)
\(660\) 7.97247e10i 0.420162i
\(661\) −4.18994e10 −0.219484 −0.109742 0.993960i \(-0.535002\pi\)
−0.109742 + 0.993960i \(0.535002\pi\)
\(662\) 2.93621e11i 1.52882i
\(663\) 3.88542e10i 0.201087i
\(664\) 1.20378e11 0.619265
\(665\) 1.39954e11 0.715648
\(666\) −2.59617e10 −0.131958
\(667\) 1.39329e10i 0.0703947i
\(668\) 4.33667e10 0.217796
\(669\) −1.95386e11 −0.975415
\(670\) −9.88291e10 −0.490440
\(671\) −3.01299e11 −1.48630
\(672\) 6.04805e10i 0.296577i
\(673\) 2.42999e11i 1.18453i −0.805745 0.592263i \(-0.798235\pi\)
0.805745 0.592263i \(-0.201765\pi\)
\(674\) 2.57832e11 1.24939
\(675\) 2.20018e10 0.105985
\(676\) −8.47553e10 −0.405864
\(677\) −2.40852e11 −1.14655 −0.573277 0.819361i \(-0.694328\pi\)
−0.573277 + 0.819361i \(0.694328\pi\)
\(678\) −1.40634e11 −0.665535
\(679\) 1.04443e10i 0.0491360i
\(680\) 1.64236e11i 0.768126i
\(681\) 2.21874e10i 0.103162i
\(682\) 3.16227e11i 1.46171i
\(683\) 2.86451e11i 1.31634i −0.752870 0.658169i \(-0.771331\pi\)
0.752870 0.658169i \(-0.228669\pi\)
\(684\) −3.31681e10 −0.151529
\(685\) −4.42003e11 −2.00753
\(686\) 2.61880e11i 1.18251i
\(687\) 1.65465e10i 0.0742811i
\(688\) 1.23648e11i 0.551867i
\(689\) 3.11028e10i 0.138014i
\(690\) 1.17714e11 0.519318
\(691\) 1.05033e11i 0.460694i 0.973109 + 0.230347i \(0.0739861\pi\)
−0.973109 + 0.230347i \(0.926014\pi\)
\(692\) 6.71453e10i 0.292814i
\(693\) 5.67989e10i 0.246267i
\(694\) −1.01443e11 −0.437303
\(695\) −8.46645e9 −0.0362879
\(696\) 1.03133e10i 0.0439500i
\(697\) −7.11054e10 −0.301281
\(698\) 8.09875e10 0.341190
\(699\) 2.12528e11i 0.890240i
\(700\) −3.65911e10 −0.152400
\(701\) 8.98668e10i 0.372158i 0.982535 + 0.186079i \(0.0595780\pi\)
−0.982535 + 0.186079i \(0.940422\pi\)
\(702\) −2.06135e10 −0.0848796
\(703\) 7.75411e10i 0.317476i
\(704\) 6.03674e10i 0.245760i
\(705\) 1.87428e10i 0.0758713i
\(706\) −5.83419e11 −2.34834
\(707\) 1.79927e10i 0.0720143i
\(708\) −6.14432e10 + 2.88340e10i −0.244535 + 0.114755i
\(709\) −1.33687e11 −0.529060 −0.264530 0.964377i \(-0.585217\pi\)
−0.264530 + 0.964377i \(0.585217\pi\)
\(710\) 7.09242e11i 2.79101i
\(711\) −3.43881e10 −0.134564
\(712\) 2.76161e11 1.07459
\(713\) 1.48823e11 0.575853
\(714\) 1.02876e11i 0.395842i
\(715\) −1.47987e11 −0.566237
\(716\) 1.51258e10i 0.0575527i
\(717\) −1.81701e10 −0.0687511
\(718\) 4.61864e11i 1.73786i
\(719\) 3.90817e11i 1.46237i −0.682177 0.731187i \(-0.738967\pi\)
0.682177 0.731187i \(-0.261033\pi\)
\(720\) −1.39324e11 −0.518436
\(721\) 1.53991e11i 0.569841i
\(722\) 1.84214e10i 0.0677914i
\(723\) 1.96600e11 0.719499
\(724\) −1.45094e11 −0.528076
\(725\) −1.79652e10 −0.0650250
\(726\) 1.08862e11i 0.391858i
\(727\) 2.67882e11 0.958973 0.479486 0.877549i \(-0.340823\pi\)
0.479486 + 0.877549i \(0.340823\pi\)
\(728\) −3.89915e10 −0.138817
\(729\) 1.04604e10 0.0370370
\(730\) −2.28355e11 −0.804116
\(731\) 1.20713e11i 0.422752i
\(732\) 9.22831e10i 0.321424i
\(733\) −1.00091e11 −0.346722 −0.173361 0.984858i \(-0.555463\pi\)
−0.173361 + 0.984858i \(0.555463\pi\)
\(734\) 3.63216e11 1.25135
\(735\) −1.36418e11 −0.467436
\(736\) −1.51935e11 −0.517781
\(737\) −1.19795e11 −0.406039
\(738\) 3.77239e10i 0.127172i
\(739\) 3.87711e11i 1.29996i −0.759951 0.649980i \(-0.774777\pi\)
0.759951 0.649980i \(-0.225223\pi\)
\(740\) 5.70857e10i 0.190371i
\(741\) 6.15674e10i 0.204210i
\(742\) 8.23524e10i 0.271682i
\(743\) 3.02109e11 0.991308 0.495654 0.868520i \(-0.334928\pi\)
0.495654 + 0.868520i \(0.334928\pi\)
\(744\) −1.10160e11 −0.359527
\(745\) 1.13881e11i 0.369679i
\(746\) 3.59877e11i 1.16198i
\(747\) 9.96949e10i 0.320177i
\(748\) 1.75033e11i 0.559132i
\(749\) −1.10384e11 −0.350734
\(750\) 1.23828e11i 0.391356i
\(751\) 2.88819e11i 0.907959i −0.891012 0.453979i \(-0.850004\pi\)
0.891012 0.453979i \(-0.149996\pi\)
\(752\) 4.21497e10i 0.131802i
\(753\) −1.47707e11 −0.459431
\(754\) 1.68316e10 0.0520763
\(755\) 1.35052e11i 0.415637i
\(756\) −1.73966e10 −0.0532570
\(757\) −5.13648e11 −1.56416 −0.782082 0.623176i \(-0.785842\pi\)
−0.782082 + 0.623176i \(0.785842\pi\)
\(758\) 1.17647e11i 0.356374i
\(759\) 1.42686e11 0.429947
\(760\) 2.60244e11i 0.780058i
\(761\) −3.41151e11 −1.01720 −0.508601 0.861002i \(-0.669837\pi\)
−0.508601 + 0.861002i \(0.669837\pi\)
\(762\) 4.87015e10i 0.144451i
\(763\) 3.42651e10i 0.101101i
\(764\) 9.52077e10i 0.279446i
\(765\) −1.36017e11 −0.397143
\(766\) 4.52250e11i 1.31360i
\(767\) −5.35223e10 1.14052e11i −0.154651 0.329551i
\(768\) 2.29833e11 0.660644
\(769\) 3.32287e11i 0.950183i 0.879936 + 0.475092i \(0.157585\pi\)
−0.879936 + 0.475092i \(0.842415\pi\)
\(770\) −3.91832e11 −1.11465
\(771\) 1.04076e10 0.0294532
\(772\) 4.88654e10 0.137573
\(773\) 3.98928e11i 1.11732i 0.829397 + 0.558659i \(0.188684\pi\)
−0.829397 + 0.558659i \(0.811316\pi\)
\(774\) 6.40426e10 0.178445
\(775\) 1.91893e11i 0.531927i
\(776\) −1.94211e10 −0.0535583
\(777\) 4.06701e10i 0.111581i
\(778\) 2.20623e11i 0.602187i
\(779\) 1.12672e11 0.305961
\(780\) 4.53259e10i 0.122453i
\(781\) 8.59701e11i 2.31070i
\(782\) −2.58438e11